You don't need to Accept anything; that is a Convenience tool. For instance, you mark it to Ignore and it gets deleted from Banking. Or, it never existed in Banking. You have full control; you are the human.

"I need the new deposit and the reissued check to cancel each other out ...  and need entries to be precise and correct ...."

Yes, that is covered in this topic:
Make a deposit entry for the Bounce, and post that as going to Liability = you still owe it to someone. This deposit and the original check apply against each other and net to 0 = No Impact on banking.

Then, Pay that out again, to the right name, and you are paying out the Liability = these still are not your funds, and this still is not More Expense.